Perez enjoyed a solid start to the year with three podiums in four races, all runner-up spots to Verstappen.
Those performances have strengthened his position within the team as it is weighing up whether to renew the Mexican's expiring contract or bring in new blood for 2025 and beyond, with plenty of free agents on the market for next year.
Last year, Perez appeared to struggle under his own expectations of being able to match Verstappen, with two early wins igniting early world-title aspirations.
But Horner felt Perez adjusting his mindset for this season, by no longer being focused on what Verstappen is doing, has made him more relaxed behind the wheel.
"You guys have a tendency to write him off but he is doing a great job," Horner told Sky Sports F1.
"He has come into this season with a new frame of mind, he is relaxed, he is driving the car really well.
"He is not focused on his team-mate, it is a different approach and in the first five races we’ve seen a really strong performance from him.
"He is driving well, his confidence is growing and hopefully he can convert that into another good result tomorrow."
Horner added that Perez is responding well to the pressure of fighting for his future at the team following his winter reset.
"He is an important part of the team and it is about working collectively and I think he has got a great engineering support around him and the team are doing a good job," he explained.
Source: Autosport